Question

Question: A certain orthodontist uses a wire brace to align a patient’s crooked tooth as in Figure P5.4. The tension in the wire is adjusted to have a magnitude of $\mathbf{18}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{N}$. Find the magnitude of the net force exerted by the wire on the crooked tooth.

Short answer

The magnitude of the net force exerted by the wire on the crooked tooth is $8.71\mathrm{N}$.

Step-by-step solution

Identification of given data

The horizontal components of the tension in the wire get cancelled due to the opposite direction. The magnitude of the resultant force exerted by wire is only due to the vertical component of tension.

Consider the given data as below.

The magnitude of tension in the wire, $T=18\mathrm{N}$

The angle of the wire from horizontal, $\theta ={14}^o$.

 Step 2: Determination of magnitude of the net force exerted by the wire on the crooked tooth

Themagnitude of the net force exerted by the wire on the crooked toothis given as

$F=2T\sin \theta$

Substitute all the values in the above equation.

$\begin{array}{rcl}\mathrm{F}& =& 2\times 18\mathrm{N}\times \sin {14}^{\circ }\\ & =& 36\mathrm{N}\times 0.242\\ & =& 8.71\mathrm{N}\end{array}$

Hence, the magnitude of the net force exerted by the wire on the crooked tooth is$\begin{array}{rcl}& & 8.71\mathrm{N}\end{array}$.